Transcription of Parameter Estimation - ML vs. MAP - fu-berlin.de
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Parameter Estimation - ML vs. MAP - fu-berlin.de
ParameterEstimationPeter NRobinsonEstimatingParametersfrom DataMaximumLikelihood(ML)EstimationBetad istributionMaximum aposteriori(MAP)EstimationMAQP arameter EstimationML vs. MAPP eter N RobinsonDecember 14, 2012 ParameterEstimationPeter NRobinsonEstimatingParametersfrom DataMaximumLikelihood(ML)EstimationBetad istributionMaximum aposteriori(MAP)EstimationMAQE stimating parameters from DataIn many situations in bioinformatics, we want to estimate op-timal parameters from data. In the examples we have seen inthe lectures on variant calling, these parameters might be theerror rate for reads, the proportion of a certain genotype, theproportion of nonreference bases etc. However, the hello worldexample for this sort of thing is the coin toss, so we will startwith NRobinsonEstimatingParametersfrom DataMaximumLikelihood(ML)EstimationBetad istributionMaximum aposteriori(MAP)EstimationMAQCoin tossLet s say we have two coins that are each tossed 10 timesCoin 1: H,T,T,H,H,H,T,H,T,TCoin 2: T,T,T,H,T,T,T,H,T,TIntuitively, we might guess that coin one is a fair coin, ,P(X=H) = , and that coin 2 is biased, ,P(X=H)6= NRobinsonEstimatingParametersfrom DataMaximumLikelihood(ML)EstimationBetad istributionMaximum aposteriori(MAP)EstimationMAQD iscrete random VariableLet us begin to formalize this.
Random variables are either discrete (i.e., they can assume one of a list of values, like the Bernoulli with heads/tails) or con-tinuous (i.e., they can take on any numerical value in a certain interval, like the Beta distribution with ). A probability density function (pdf) of a continuous random variable, is a function that describes the relative
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